Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11	, , , ⊢
	: , : , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	42	⊢
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	instantiation	12	⊢
	: , :
6	instantiation	12	⊢
	: , :
7	instantiation	13, 14, 15	⊢
	: , :
8	instantiation	44, 27, 16	⊢
	: , : , :
9	instantiation	17, 18, 19, 20	⊢
	: , :
10	instantiation	44, 27, 21	⊢
	: , : , :
11	instantiation	44, 27, 22	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
14	instantiation	44, 27, 23	⊢
	: , : , :
15	instantiation	44, 27, 24	⊢
	: , : , :
16	instantiation	44, 32, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	instantiation	44, 27, 26	⊢
	: , : , :
19	instantiation	44, 27, 28	⊢
	: , : , :
20	instantiation	29, 30	⊢
	:
21	instantiation	44, 32, 31	⊢
	: , : , :
22	assumption		⊢
23	instantiation	44, 32, 33	⊢
	: , : , :
24	instantiation	44, 36, 34	⊢
	: , : , :
25	assumption		⊢
26	instantiation	44, 36, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	44, 36, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
33	assumption		⊢
34	instantiation	44, 40, 38	⊢
	: , : , :
35	instantiation	44, 40, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	44, 40, 41	⊢
	: , : , :
38	instantiation	44, 45, 42	⊢
	: , : , :
39	instantiation	44, 45, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	44, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3